New Constructions of Orthogonal Product Basis Quantum States



An orthogonal basis \({\mathcal {B}}_{9}\) for the Hilbert space C3 × C3 was presented by Bennett et al. (Phys. Rev. A 59, 1070, 1999) which was illustrated in a visual figure in their report. The character of the construction is that each base vector is a product state, thus any distinguishing operator cannot create entanglement. In this paper, we mainly focus on some new constructions of orthogonal product basis quantum states in the high-dimensional quantum systems. Especially, as for the quantum system of (2m + 1) ⊗ (2m + 1), where mZ and m ≥ 2, we have provided the direct construction in mathematical method.


New constructions Orthogonal product basis Hadamard matrix High-dimensional quantum systems 



This work is supported by NSFC (Grant Nos. 61402148,61601171), Natural Science Foundation of Hebei Province (F2015205114), Doctoral Scientific Fund Project of Hebei Normal University (F2016B05).


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Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangChina
  2. 2.School of Mathematics and Information ScienceHenan Polytechnic UniversityJiaozuoChina

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